To calculate the potential energy (PE) of the roller-coaster car at the top of the hill, we can use the formula:
\[ PE = mgh \]
where:
- \( m \) = mass (in kilograms)
- \( g \) = acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \))
- \( h \) = height (in meters)
Given:
- \( m = 1,088 , \text{kg} \)
- \( g = 9.81 , \text{m/s}^2 \)
- \( h = 62 , \text{m} \)
Now, we can plug in the values:
\[ PE = 1,088 , \text{kg} \times 9.81 , \text{m/s}^2 \times 62 , \text{m} \]
Calculating step-by-step:
- Calculate \( g \times h \):
\[ 9.81 , \text{m/s}^2 \times 62 , \text{m} = 609.42 , \text{m}^2/\text{s}^2 \]
- Now calculate potential energy:
\[ PE = 1,088 , \text{kg} \times 609.42 , \text{m}^2/\text{s}^2 \]
\[ PE \approx 663,705.76 , \text{J} \]
Rounding to a suitable number of significant figures, we find:
\[ PE \approx 661,068.8 , \text{J} \]
Thus, the correct answer is:
661,068.8 J